Section: New Results

Regular Patterns in Second-Order Unification

Participant : Tomer Libal.

We presented a paper [33] detailing a higher-order pre-unification procedure with improved termination over existing procedures. The classic higher-order unification procedure was presented by G. Huet in 1975 and is still used as the main unification procedure for higher-order automated theorem provers. This procedure does not terminate. In this project we have investigated the reasons for that and have shown that by choosing a specific (but complete) search strategy, an additional set of non-unifiable problems can be detected. As an example, we have shown that all unification problems generated by the Leo-III theorem prover when proving Cantor's theorem are decided by this procedure, in contrast to the classical unification procedure.